Simplify the following expression: $k = \dfrac{r^2 + 7r + 10}{r + 5} $
Answer: First factor the polynomial in the numerator. $ r^2 + 7r + 10 = (r + 5)(r + 2) $ So we can rewrite the expression as: $k = \dfrac{(r + 5)(r + 2)}{r + 5} $ We can divide the numerator and denominator by $(r + 5)$ on condition that $r \neq -5$ Therefore $k = r + 2; r \neq -5$